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A153177
a(n) = L(9*n)/L(n) where L(n) = Lucas number A000204(n).
5
76, 1926, 109801, 4769326, 230701876, 10716675201, 505618944676, 23714405408926, 1114769987764201, 52357935173823126, 2459933168462154076, 115560463558534156801, 5428954301161174383676, 255043991670277234750326
OFFSET
1,1
COMMENTS
All numbers in this sequence are:
congruent to 1 mod 100 (iff n is congruent to 0 mod 3),
congruent to 26 mod 100 (iff n is congruent to 2 or 4 mod 6),
congruent to 76 mod 100 (iff n is congruent to 1 or 5 mod 6).
LINKS
Index entries for linear recurrences with constant coefficients, signature (34,714,-4641,-12376,12376,4641,-714,-34,1).
FORMULA
From R. J. Mathar, Oct 22 2010: (Start)
a(n) = 34*a(n-1) +714*a(n-2) -4641*a(n-3) -12376*a(n-4) +12376*a(n-5) +4641*a(n-6) -714*a(n-7) -34*a(n-8) +a(n-9).
G.f.: -x*(76-658*x-9947*x^2+13644*x^3+26020*x^4-5306*x^5-1372*x^6+42*x^7 +x^8) / ((x-1)*(x^2+18*x+1)*(x^2-47*x+1)*(x^2+3*x+1)*(x^2-7*x+1)).
a(n) = 1-(-1)^n*A087215(n) -(-1)^n*A005248(n) +A056854(n) +A087265(n). (End)
MATHEMATICA
Table[LucasL[9*n]/LucasL[n], {n, 1, 50}]
LinearRecurrence[{34, 714, -4641, -12376, 12376, 4641, -714, -34, 1}, {76, 1926, 109801, 4769326, 230701876, 10716675201, 505618944676, 23714405408926, 1114769987764201}, 20] (* Harvey P. Dale, Aug 12 2012 *)
PROG
(PARI) {lucas(n) = fibonacci(n+1) + fibonacci(n-1)};
for(n=0, 30, print1( lucas(9*n)/lucas(n), ", ")) \\ G. C. Greubel, Dec 21 2017
(Magma) [Lucas(9*n)/Lucas(n): n in [0..30]]; // G. C. Greubel, Dec 21 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Artur Jasinski, Dec 20 2008
STATUS
approved